On the dynamics of transversely holomorphic flows on closed 3-manifolds

In this paper, we study several dynamical properties of the transversely holomorphic flows $\cL$ on a closed 3-manifold $M$ with a certain cohomology condition $H^2(M,\cO)\neq0$. For such a flow, we prove the nonhyperbolicity, nonshadowability and non-expansivity of $M$, and find the detailed description of recurrence points, $\omega$-limit sets and attractors on $M$.